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Light Scattering Through the Eyes of the Singularity Expansion Method

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MWSW01 - Canonical scattering problems

Isam Ben Soltane, Rémi Colom, Brian Stout, Nicolas Bonod Light can be reflected, transmitted, scattered, or diffracted by optical components. Knowledge of such optical responses is fundamental for optical component design and the tailoring of light-matter interactions. Optical response is typically studied in either the time or harmonic domains. In the time domain, the scattered field can be described through transient and steady states, while in the harmonic domain, the spectral response features resonances that are of crucial interest for enhancing the light matter interactions. When monitoring the optical response as a function of the frequency, resonances typically appear in the form of sharp maxima. When extending the optical response to the complex frequency plane, one finds singularities, for which the optical response becomes infinite. A fundamental question that has attracted attention for several decades is to establish how these singularities in the complex plane influence the response of optical systems at real frequencies and the extent to which this response, is fully predicted by these singularities, for both time and harmonic domains. This method is called Singularity Expansion Method (SEM) [1,2].   In this talk, we first present the fundamentals of this method and then show how a simplified expression of the expansion, the Approximate Singularity Expansion (ASE), is convenient and accurate for studying optical responses in both harmonic and time domains. We also show how the ASE method can predict the optical response of plasmonic metasurfaces and resonant light scattering of sub-wavelength sized particles [3-5]. The convergence of this method is verified for these different configurations in terms of the number of singularities considered. In a second step, we will consider a Fabry-Perot 1D optical cavity to apply this expansion to the Fresnel coefficients [6]. This allows a derivation of the singularity expansion of the Impulse Response Function (IRF), by which the response in the time domain can be retrieved by a convolution with the excitation field. We point out the importance of causality that prevents divergence of the expansion [5-7]. We then analyse the steady and transient states expansions and their link with the singularities. In a third and final step, we show how the SEM can be generalized to the case of singularities of arbitrary order [8] and will discuss the perspectives of this method. References [1] C. E. Baum, “On the singularity expansion method for the solution of electromagnetic interaction problems,” Tech. rep. AIR FORCE WEAPONS LAB KIRTLAND AFB NM (1971) [2] P. Vincent, “Singularity expansions for cylinders of finite conductivity,” Applied Physics 17, 239–248 (1978) [3] V. Grigoriev, A. Tahri, S. Varault, B. Rolly, B. Stout, J. Wenger, N. Bonod, “Optimization of resonant effects in nanostructures via Weierstrass factorization,” Phys. Rev. A 88 , 011803® (2013) [4] V. Grigoriev, S. Varault, G. Boudarham, B. Stout, J. Wenger, N. Bonod, “Singular analysis of Fano resonances in plasmonic nanostructures,” Phys. Rev. A 88 , 063805 (2013) [5] R. Colom, R. C. McPhedran, B. Stout, N. Bonod, “Modal Expansion of the scattered field : Causality, Non-Divergence and Non-Resonant Contribution,” Phys. Rev. B 98 , 085418 (2018) [6] I. Ben Soltane, R. Colom, B. Stout, N. Bonod, “Derivation of the Transient and Steady Optical States from the Poles of the S-Matrix,” Lasers Photonic Rev., 2200141 (2022) [7] I. Ben Soltane, R. Colom, F. Dierick, B. Stout, N. Bonod, “ Multiple-Order Singularity Expansion Method,” arXiv (2023)

This talk is part of the Isaac Newton Institute Seminar Series series.

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